Problem: The sum of the digits of the year 2004 is 6. What is the first year after 2000 for which the sum of the digits is 12?
Explanation: To find the first year after $2000$ for which the sum of the digits is $12$, take the greatest possible units digit, $9$. $2+9=11$, so take $1$ as the tens digit and $0$ as the hundreds digit. The answer is therefore $\boxed{2019}$.